What question did this study set out to answer?

The aim is to explore conditions for the existence and stability of monotonic solutions in fractional quadratic integral equations.

April 15, 2026Open Access

Non-Decreasing Solutions for (k,Υ)-Fractional Quadratic Integral Equations of Urysohn–Volterra Type

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Key Points

The aim is to explore conditions for the existence and stability of monotonic solutions in fractional quadratic integral equations.
Investigated (k,Υ) fractional quadratic integral equations in a Banach space.
Applied a measure of noncompactness related to monotonicity.
Utilized Darbo’s fixed point theorem for analysis.
Provided sufficient conditions for at least one monotonic solution.
Analyzed the stability of the monotonic solution.
Presented an illustrative example to support theoretical findings.

Abstract

In this paper, we investigate a (k,Υ) fractional quadratic integral equation in the Banach space of real-valued continuous functions on 0,1. By using a measure of noncompactness associated with monotonicity and Darbo’s fixed point theorem, we provide sufficient conditions for the existence of at least one monotonic solution and analyze its stability. Finally, an illustrative example is presented to demonstrate the theoretical results, including several particular cases.

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El-Malty et al. (Mon,) studied this question.

synapsesocial.com/papers/69df2b85e4eeef8a2a6b07f1 — DOI: https://doi.org/10.3390/fractalfract10040256

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Authors

Shahenda S. El-Malty

Alexandria University

Mahmoud Mohamed El-Borai

Alexandria University

Wagdy G. El-Sayed

Alexandria University

Journals

Fractal and Fractional

Actions

Institutions

Alexandria University

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Non-Decreasing Solutions for (k,Υ)-Fractional Quadratic Integral Equations of Urysohn–Volterra Type

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

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Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Also consider